Core Flow Research Articles

Effects of the Librationally Induced Flow in Mercury’s Fluid Core with an Outer Stably Stratified Layer

Observational constraints on Mercury’s thermal evolution and magnetic field indicate that the top part of the fluid core is stably stratified. Here we compute how a stable layer affects the core flow in response to Mercury’s main 88 day longitudinal libration, assuming various degrees of stratification, and study whether the core flow can modify the libration amplitude through viscous and electromagnetic torques acting on the core–mantle boundary (CMB). We show that the core flow strongly depends on the strength of the stratification near the CMB but that the influence of core motions on libration is negligible with or without a stably stratified layer. A stably stratified layer at the top of the core can, however, prevent resonant behavior with gravito-inertial modes by impeding radial motions and promote a strong horizontal flow near the CMB. The librationally driven flow is likely turbulent and might produce a nonaxisymmetric induced magnetic field with a strength of the order of 1% of Mercury’s dipolar field.

Numerical study on the flow and heat transfer characteristics in a high-temperature gas-cooled reactor core

In the high-temperature gas-cooled reactor (HTGR), the core operation heavily relies on the heat transfer process facilitated by the coolant that withdraws the heat released by fuel particles. Therefore, it is imperative to carefully study the flow and heat transfer characteristics between the fuel particle and coolant. Additionally, under high core temperature conditions, the fuel particle tends to incur damage. In this study, we have designed a new type of HTGR using hydrogen as a coolant, and performed numerical simulations to explore the flow and heat transfer conditions in the core under various working conditions. Our results indicate that under high velocity inlet and low temperature inlet conditions, the system provides a high heat transfer rate. Furthermore, interesting relationships were observed between the flow and heat transfer characteristics of the model through the Reynolds number (Re), n, and Tr. Since the density of the coolant changes as the temperature varies, the hydrogen is susceptible to compression. Notably, poor thermal conductivity on the fuel particle surface generates hotspots at the points of flow stagnation, flow separation, and flow convergence. Our study on the new reactor core's flow and heat transfer characteristics provides an important reference for improving the core outlet temperature and the fuel particle's structure.

A mist-based crosslinking technique for coaxial bioprinting of hollow hydrogel fibers

In this paper, a mist-based method for coaxial three-dimensional bioprinting of ionically crosslinking hydrogel hollow fibers is presented. Unlike current techniques of coaxial bioprinting that utilize the crosslinker in liquid or sacrificial form, the developed method introduces the core crosslinking agent in mist form. The use of mist as a core flow provides adequate pressure and sufficient crosslinking to maintain the tubular shape of a hollow fiber. Through controlled exposure of crosslinker, the developed system prevents poor resolution and layer adhesion caused by the accumulation of liquid crosslinker on the printbed. Furthermore, it eliminates additional processing steps, such as partial crosslinking of the hydrogel prior- or removal of sacrificial material post-printing. The printability and mechanical properties of hollow fiber scaffolds printed using various mist and hydrogel concentrations are studied. It is shown that mist concentration influences the gelation rate of the hollow fiber, impacting the shape fidelity, layer adhesion, and mechanical properties of the printed structures. Moreover, the effects of printing parameters, including the mist core pressure and hydrogel flowrate, on the diameter and wall thickness of the hollow fiber are investigated. Finally, scaffolds printed and crosslinked using mist exhibit over 90% cell viability. The developed mist-based coaxial system enables direct printing of continuous hollow fibers.

Safety considerations related to boron redistribution during Loss-of-Coolant-Accident initiated beyond design basis events for the NuScale power module

The authors, as staff at the U.S. Nuclear Regulatory Commission (NRC), evaluated the potential consequences of boron dilution under beyond design basis conditions in the NuScale Power Module to inform NRC staff’s safety evaluation report for the NuScale design certification review. The authors identified the small break loss of coolant accident with coincident failure of control rods to insert as the scenario with the most adverse boron dilution and reactivity insertion consequences. The authors evaluated the sequence of events for the scenario to determine which conditions or phenomena could produce the potential for a core flow surge to yield core damage because of a super-prompt reactivity excursion. The authors screened the conditions and phenomena that could potentially cause a core flow surge based on the dynamic speed of the incursion compared to key reactivity feedback mechanisms: thermal–hydraulic coupling via rod heat transfer and convective mixing. Based on the screening process, the authors were able to identify two processes that could potentially lead to a power excursion. However, the authors’ analysis relies heavily on assumptions regarding convective mixing, making this an important phenomenon worth careful consideration in any evaluation of boron redistribution.

Parametric dependence and elementary modelling for compressor disc cavity heat transfer

A wall-modelled large-eddy simulation (WMLES) method previously validated against laboratory experiments is applied to a real engine disc cavity geometry with surface and air temperatures representative of maximum power conditions. An appropriate set of independent nondimensional parameters describing the problem is defined and the sensitivities to these parameters are investigated by independently varying each parameter in the WMLES. Effects of a change in disc temperature distribution and a reduction in radius of the downstream disc are also investigated. The flow and heat transfer mechanisms predicted are very similar to those found for the research rig configuration although rotating cavity flow structures with two or more lobes are found for the engine geometry rather than the single-lobed structures shown in previous work. The simulations are compared with an elementary model giving further insight into scaling of the flow and heat transfer with operating conditions. The model assumes a well-mixed core flow in the cavity with constant rothalpy, relates shroud heat transfer to that of natural convection under gravity for high Rayleigh number, and relates disc heat transfer to conduction across unsteady Ekman layers. An energy balance for the cavity is used to obtain an effective mass flow exchange rate between the axial throughflow and the disc cavity to the disc and shroud heat transfer and core temperature. The model is considered to give a useful basis for engineering calculations involving correlation and extrapolation of WMLES and experimental results.

Exploration of transient flow perturbations in a bulb turbine diffuser using proper orthogonal decomposition

Hydraulic turbines with high efficiency over a wide range of operating conditions offer a much sought-after flexibility to electricity producers. However, some low-head turbines exhibit sharp losses of efficiency close to their peak efficiency discharge that are linked to draft tube flow separations whose causes remain misunderstood. This paper presents the latest results obtained in the scope of the BulbT project that focused on the flow dynamics related to the efficiency drop. The main objectives are to document the transient characteristics of the flow in the hub-wake region and investigate interactions between the core flow and wall separations to identify potential mechanisms explaining the efficiency drop. Using proper orthogonal decompositions of synchronized time-resolved velocity and pressure measurements, highly energetic modes representing stochastic perturbations across BulbT's draft tube are identified. These perturbations occur only for the discharges affected by the efficiency drop, past the best efficiency point. Despite the absence of near-wall velocity measurements, the modal decompositions provide evidence that the onset of the efficiency drop is the result of two independent types of flow separation that occur on opposite sides of the draft tube. Upstream separations are found to happen simultaneously with an asymmetric acceleration of the flow in a region surrounding the turbine's axis and the tip of the runner hub and become the most important contributor to the efficiency drop at the highest measured flow rate. Furthermore, the likeliness of observing one kind of flow separation increases after it has already occurred, pointing to a strong history effect.

Polar ionospheric currents and high temporal resolution geomagnetic field models

SUMMARY Estimating high resolution models of the Earth’s core magnetic field and its time variation in the polar regions requires that one can adequately account for magnetic signals produced by polar ionospheric currents, which vary on a wide range of time and length scales. Limitations of existing ionospheric field models in the challenging polar regions can adversely affect core field models, which in turn has important implications for studies of the core flow dynamics in those regions. Here we implement a new approach to co-estimate a climatological model of the ionospheric field together with a model of the internal and magnetospheric fields within the CHAOS geomagnetic field modelling framework. The parametrization of the ionospheric field exploits non-orthogonal magnetic coordinates to efficiently account for the geometry of the Earth’s magnetic field and scales linearly with external driving parameters related to the solar wind and the interplanetary magnetic field. Using this approach we derive a new geomagnetic field model from measurements of the magnetic field collected by low Earth orbit satellites, which in addition to the internal field provides estimates of the typical current system in the polar ionosphere and successfully accounts for previously unmodelled ionospheric signals in field model residuals. To resolve the ambiguity between the internal and ionospheric fields when using satellite data alone, we impose regularization. We find that the time derivative of the estimated internal field is less contaminated by the polar currents, which is mostly visible in the zonal and near-zonal terms at high spherical harmonic degrees. Distinctive patches of strong secular variation at the core–mantle boundary, which have important implications for core dynamics, persist. Relaxing the temporal regularization reveals annual oscillations, which could indicate remaining ionospheric field or related induced signals in the internal field model. Using principal component analysis we find that the annual oscillations mostly affect the zonal low-degree spherical harmonics of the internal field.

Study on Optimum Selection Method of Additives for Slick-Water Fracturing Fluid

In order to clarify the research idea of fluid system optimization in slick-water fracturing, a scientific and effective single-agent optimization method was selected to study the performance optimization method and performance evaluation method of drag reducer, clay stabilizer and cleanup additive in slick-water fracturing fluid. The specific experimental steps and application examples were investigated. To select the drag reducer, the drag reduction rate rate of the drag reducer at different concentrations should be measured first, the optimal concentration of a single agent should be selected, and then the stability test of temperature, flow rate and shear time should be performed on the optimal concentration of a single agent, and finally the combination formula with high drag reduction rate rate and stable performance can be selected. To optimize the clay stabilizer, the optimal concentration of single agent should be obtained by measuring the anti-swelling rate of different single agent and different concentration, and then the anti-swelling rate of each compound formula should be determined according to the optimal concentration of single agent, and finally the anti-swelling performance of the composite combination should be evaluated according to the core flow experiment. The optimal concentration of a single agent should first be optimized according to the surface tension of the cleanup additive, and then the combined formula should be optimized according to the surface tension of the combined combination, and the cleanup additive ability should be evaluated by core spontaneous imbibition or measuring the increase rate of cleanup additive.

Thermal behaviors and flow profiles in a square channel fitted with X–V modified ribs: A numerical analysis

A novel design of “X–V rib” turbulators is proposed to improve fluid blending and to perturb thermal boundary layer (TBL) in a heat exchanger (HX) duct. Better fluid blending and more highly disturbed TBL are the two important factors for the improvement of HX performance. Effects of X–V rib geometrical parameters including rib height ratios (b/H = 0.05–0.20), rib arrangements (V-tip pointing upstream called “V-Upstream (VU)” and V-tip pointing downstream called “V-Downstream (VD)”) and rib types (I, II and III) on air stream and thermal mechanisms are numerically investigated in a 3D model. The numerical model is solved with the finite volume method (a commercial code) and a commercial program. Laminar air flow (inlet conditions with Re = 100–2000) is a selected range of the present investigation. Firstly, the created numerical model for the ribbed duct is validated with two significant topics: 1. Plain duct validation and 2. Optimum grid elements (grid independence). The validated results show that the ribbed-duct model has great reliability to simulate air stream and thermal characteristics. According to the numerical results, the disturbed TBL is obviously found in all rib types. Moreover, it is observed that the core flow disturbance occurs and improves fluid blending. The outcomes from the present investigation point out that the knowledge about flow structure and thermal mechanism are important guidelines for the development of vortex turbulators and HX improvement. For the thermal assessments, it is found that the best Nusselt number ratio (Nu/Nu0) is 11.80 for the type III X–V rib with b/H = 0.20 in the VD-direction. Additionally, the maximum thermal enhancement factor within our investigated range is 3.48 at Re = 2000, b/H = 0.20, type II X–V rib in the VU-direction.

Numerical simulation for MEOR considering the size effect between microorganisms and porous media

Based on the analysis of size effect between microorganisms and porous media, a one-dimensional two-phase, five-component mathematical model was presented to simulate the process of microbial flooding. The components of this mathematical model consist of oil, water, microorganisms, nutrients and metabolites, wherein the main metabolite is biopolymer. The transport equations not only consider the characteristics of microbial growth, death, chemotaxis, convection-dispersion, and adsorption-desorption, but also consider the straining behavior and the behavior of products that cannot pass through all pore areas which are caused by the size effect of microorganisms and products. This newly developed model is validated with a classical simulator and a core flow experiment. In this study, the sensitivity of the straining coefficient and product inaccessible volume were analyzed through a simulator developed according to our mathematical model. We found that: (1) The straining deposition will be much larger than the adsorption deposition; (2) The straining behavior which is caused by the size effect of bacteria has a great influence on the microbial concentration and the oil recovery; (3) The product inaccessible volume caused by the size effect of product has a significant effect on the distribution of product concentration, but has little impact on the oil recovery.

An active mixing enhancement technique in supersonic ejectors using pulsed streamwise injections

The current study numerically investigates an active mixing enhancement technique for a supersonic ejector with a constant area mixing chamber operating under the critical regime. Streamwise control jet injections are alternatively pulsed at the top and bottom sides of the mixing chamber entrance. The induced oscillation of the primary jet enhances the bulk mixing between the primary and secondary streams. The secondary stream penetrates the primary core flow much upstream with the control strategy compared to the no-injection case, improving the onset of mixing by 65.36%. A higher spread of the primary jet along the mixing chamber height is observed with the control strategy indicating an enhanced mixing between the two streams. Dynamic mode decomposition analysis of the fluctuations of the velocity magnitude revealed that the dominant dynamic structures are determined by the pulsation frequency and a dominant flapping mode can be observed. The frequency spectrum of the primary jet oscillation revealed that the dominant frequency of oscillation is dictated by the pulsation frequency of the injection. With an increase in the control jet pulsation frequency, the amplitude of primary jet oscillation reduces near the entrance region of the mixing chamber, whereas the amplitude of oscillation far downstream reaches nearly the same value for all the cases. The power spectral analysis of the unsteady pressure fluctuations along the mixing chamber wall revealed that the wall pressure oscillations are contributed by the control jet pulsation frequency as well as the shock wave reflections produced by the supersonic jet–jet interaction within the mixing chamber.

Novel water shut off method based on temporary plugging agent and gel composition

This article presents the laboratory development of a novel rigless, self-selective water shut-off technique. The technique involves the design and pumping of three different fluids through fractured core plugs in a specific sequence. The first fluid serves to temporarily block porous medium while moving freely through fractures. The second fluid is a cross-linking polymer gelant, which is injected immediately after the first fluid at a pressure below the fracture pressure of the formation to block fractures. An enzyme-based chemical breaker solution, serving as the third fluid, is evaluated for removing the filter-forming materials. The treatment and flow studies are conducted using a high-pressure, high-temperature core flow setup. In conclusion, the developed water control technology presented in this study offers a low-cost solution for fractured and high-anomaly wells. The technology is particularly effective when there is a significant permeability contrast between the oil-bearing matrix and water-conductive fractures. The results demonstrate a successful blockage of fracture, with minimal contamination of porous medium. The study also highlights important factors to consider for the field application of this technology. It is recommended to conduct customized laboratory investigations under simulated reservoir conditions prior to implementing the technology in the field. This will help optimize the treatment design and ensure its effectiveness in real-world applications. Keywords: water shut-off; temporary blocking agent; gel composition; coreflood; permeability contrast.

The Evaluation and Application of SmartGel for Deepwater Loss-Circulation Control

In view of the problem that the formation of deepwater wells in the study area leak easily, the mechanism of loss-circulation was studied in depth, and the loss-circulation plugging material SmartGel was developed with guar gum and its derivatives as the main synthetic raw materials. The gel process could be controlled by adjusting the dosage and temperature of gel accelerators. In order to adjust the gelling speed of SmartGel, GelRetarder and GelAccelerant were developed. The extrusion strength of SmartGel increased with the increase in SmartGel dose and decreased with the increase in temperature. As for the plugging performance of SmartGel, the sand bed test confirmed that the pressure capacity of SmartGel in the 80 °C sand bed can reach at least 7 MPa, which can meet the requirements of site construction. The PPT sand tray test and core flow meter simulation pore test showed that SmartGel has good bearing performance. As for the gel-breaking of SmartGel, low-temperature gel-breaking was achieved by adding the biological gel-breaking agent S100. The gel-breaking time was shortened by increasing the dose of S100; the higher the temperature, the more obvious the effect. To facilitate high-temperature gel-breaking, the post-gel-breaking method was adopted since the enzyme gel-breaking agent cannot play a role above 60 °C. The test showed that after adding 5% gel-breaking agent PF-JPC, due to gel-breaking at 80 °C, the SmartGel gel completely reduced the viscosity within 48 h. We successfully used SmartGel + 0.2% GelRetarder to stop the loss-circulation in well A and used a cored well wall to show a good gel-breaking effect.

Intradecadal variations in length of day: Coherence with models of the Earth's core dynamics

We confirm the presence of interannual oscillations of period about 5.9 and 8.5 years in the Earth's length of day (LOD), better visible after subtracting the atmospheric contribution. Continental water mass redistribution and oceanic angular momentum contribute to a lesser extent, and are furthermore mostly compensated by sea level variations. We show, using a continuous wavelet transform analysis of synthetic oscillators embedded into a random correlated noise, the limits of isolating damped signals presenting nearby periods in time series of limited duration. In particular, we emphasize the possibility that a previously documented 7.3-year oscillation could be an artefact associated with the restricted available time span covered by LOD data. Finally, we perform a wavelet coherence analysis between geodetically observed LOD changes and their prediction from geomagnetically inferred core flow models. It confirms an origin from the fluid outer core for the two signals around 5.9 and 8.5 years. A convincing coherence is also found around 3.5 and 5 years, which may reveal signatures of higher harmonics of torsional modes or of quasi-geostrophic magneto-Coriolis modes.

COMPUTATION OF THREE-DIMENSIONAL BLOOD FLOW DEVELOPMENT IN A 180∘ CURVED TUBE GEOMETRY

Computational blood flow studies are providing an increasingly important complement to clinical experiments in 21st century biomedical engineering. Motivated by probing deeper into this topic, a theoretical and numerical study is presented of the flow induced by an impulsive acceleration to steady state hemodynamics in a curved tube which is investigated as a boundary layer developing with time from the curved entrance to a straight tube (blood vessel). The transient processes are simulated with a finite volume method solution of the Navier–Stokes equations. The rapid growth of the boundary layer with the core flow is captured in the curved entrance, along the tube to an axisymmetric flow in the downstream. Secondary flow patterns, centrifugal pressures and total head contours are correlated with longitudinal velocity distributions across various sections. It is observed that the entrance zone is controlled by uniform inlet velocity and centrifugal forces. The high pressure drop in the onset flow is associated with strong acceleration which is comparable to generating systolic pressures. The simulations further indicate that a sustained increment in volumetric flow rate is necessary to maintain the pressure wave in the aorta. Furthermore, the velocity distributions are shown to approach Hagen–Poiseuille flow in the downstream zone. The complex hemodynamic characteristics are visualized effectively with computational simulations and the study demonstrates the excellent ability of this approach in elaborating critical flow details in aortic hemodynamics.

Finite element modeling of biomass hopper flow

Hoppers are widely used biomass handling devices that channel bulk biomass from storage to subsequent handling equipment. Jenike’s longstanding approach, based on the Mohr-Coulomb model, has been successfully used to design hoppers handling cohesionless granular materials such as grains and other agricultural produces. However, designing a hopper to ensure reliable biomass flow is found to be challenging due to cohesion, irregular particle shape, and bulk material elastoplasticity. This study aims to address the biomass handling engineering challenge with alternative constitutive material models concerning the flow behavior of bulk solids. Finite element modeling is an approach that allows for implementation of different material models, whose underlying constitutive theories assist in investigating the origin and manifestation of bulk mechanical behavior of granular materials. This study focuses on the incipient gravity hopper flow of two types of biomass feedstocks, i.e., ground corn stover and Douglas fir wood. Three widely used constitutive material models, i.e., Mohr-Coulomb model, modified Cam-Clay model, and Drucker-Prager/Cap model, are implemented. Using the flow pattern represented by the volume of biomass exhibiting more than 7% of axial strain (Kamath and Puri, 1999), the finite element model predicts that the bulk corn stover particulate material forms an arch, which represents a hampered transition from the static state to the dynamic flow-state out of the hopper, whereas bulk Douglas fir wood particulate material develops a reliable mass flow pattern. A laboratory scale hopper was used to experimentally determine the biomass flow conditions, which were subsequently compared with the predicted onset of flow by a finite element model (FEM). The developed FEM was found to correctly predict the initiation of mass flow for the milled Douglas fir wood, whereas corn stover was predicted to establish a strong core flow suggesting an unreliable handling characteristic. This observation aligns with the reported poor handling of milled corn stover.

Cancellations of periodic orbits for non-singular Morse–Smale flows

AbstractIn this work, we explore the dynamical implications of a spectral sequence analysis of a filtered chain complex associated to a non-singular Morse–Smale (NMS) flow $\varphi $ on a closed orientable $3$ -manifold $M^3$ with no heteroclinic trajectories connecting saddle periodic orbits. We introduce the novel concepts of cancellations and reductions of pairs of periodic orbits based on Franks’ morsification and Smale’s cancellation theorems. The main goal is to establish an algebraic-dynamical correspondence between the unfolding of this spectral sequence associated to $\varphi $ and a family of flows obtained by cancelling and reducing pairs of periodic orbits of $\varphi $ on $M^3$ . This correspondence is achieved through a spectral sequence sweeping algorithm (SSSA), which determines the order in which these cancellations and reductions of periodic orbits occur, producing a family of NMS flows that reaches a core flow when the spectral sequence converges.

Design and characterization of the Sandia free-piston reflected shock tunnel

A new reflected shock tunnel capable of generating hypersonic environments at realistic flight enthalpies has been commissioned at Sandia. The tunnel uses an existing free-piston driver and shock tube coupled to a conical nozzle to accelerate the flow to approximately Mach 9. The facility design process is outlined and compared to other ground test facilities. A representative flight-enthalpy condition is designed using an in-house state-to-state solver and piston dynamics model and evaluated using quasi-1D modeling with the University of Queensland L1d code. This condition is demonstrated using canonical models and a calibration rake. A 25-cm core flow with 4.6-MJ/kg total enthalpy is achieved over an approximately 1-ms test time. The condition was refined using analysis and a heavier piston, leading to an increase in test time. A novel high-speed molecular tagging velocimetry method is applied using in situ nitric oxide to measure the freestream velocity of approximately 3016 m/s. Companion simulation data show good agreement in exit velocity, pitot pressure, and core flow size.

Experimental Study For a Laminar Natural Convection Heat Transfer From an Isothermal Heated Square Plate With and Without Circular Hole

An experimental investigation of natural convection heat transfer from an isothermal horizontal,vertical and inclined heated square flat plates with and without circular hole, were carried out in two cases, perforated plates without an impermeable adiabatic hole "open core" and perforated plates with an impermeable adiabatic hole "closed core" by adiabatic plug. The experiments covered the laminar region with a range of Rayleih number of (1.11x106 ≤RaLo≤4.39x106 ), at Prandtle number (Pr=0.7). Practical experiments have been done with variable inclination angles from horizon (Ф=0o ,45o,90o,135oand 180o),facing upward (0o≤Ф<90o), and downward (90o≤Ф<180o). The results showed that the temperature gradient increases while the thermal boundary layer thickness decreases when Grashof number and perforation ratio (m) increase . The temperature gradient for inclined position facing upward is less than facing downward,while the thermal boundary layer thickness is greater. The temperature gradient decreases while the thermal boundary layer thickness increases for perforated plates with an adiabatic core as compared with perforated plates without an adiabatic core. The value of average Nusselt number increases with increasing perforation ratio, and Grashof number for all specimens with and without an adiabatic core, also increases by increase in inclination of plates approaching the higher value at vertical position (Ф=90o), then decreases with increasing inclination of plates till horizontal position (Ф=180o). The average Nusselt number values for perforated plates with an adiabatic core are lower than for perforated plates without an adiabatic core for all perforation ratios. Maximum heat transfer rate occurs at perforated plate with perforation ratio of (m=0.1) without adiabatic core for vertical position (Ф=90o), at a range of Grashof number (1.576x106≤GrLo≤6.292x106 ), while the rate of heat transfer decreases with increasing perforation ratio for plates with and without adiabatic core for decrease in heat transfer rate area. The rate of heat transfer forperforated plates with circular hole is more than for perforated plates with square hole at the same perforation ratios (m=0.1,0.16,0.24 and 0.36). It found that the lack of core flow decreases the overall heat transfer rate by (6.477%) . There was a good agreement for the experimental present work results compared with other pervious results .

Global banking, financial spillovers and macroprudential policy coordination

AbstractThe transmission of financial shocks and the gains from international macroprudential policy coordination are studied in a two‐region, core–periphery model with a global bank, a two‐level financial structure and imperfect financial integration. The model replicates the stylized facts associated with global banking shocks, with respect to output, credit, house prices and real exchange rate fluctuations in recipient countries, as documented empirically. Numerical experiments, based on a parametrized version of the model, show that the gains from coordination increase with the degree of financial integration, which raises the scope for spillback effects from the periphery to the core, through trade and private capital flows. However, even when coordination is Pareto‐improving, the resulting gains may be highly asymmetric across regions.